Regular Two-graphs from the Even Unimodular Lattice E8⊕E8

✍ Scribed by Viatcheslav Grishukhin

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 381 KB
• Volume: 18
• Category: Article
• ISSN: 0195-6698
• DOI: 10.1006/eujc.1996.0104

✦ Synopsis

Starting from the even unimodular lattice E 8 E 8 , one constructs odd systems (i . e . sets of vectors with odd inner products) of 546 vectors using results of Deza and Grishukhin . One studies the subsystems consisting of 36 pairs of opposite vectors spanning equiangular lines . These subsystems represent regular two-graphs . This gives 100 such two-graphs and they coincide with the first 100 in a list of 227 two-graphs generated by E . Spence . Using the root systems of the sublattices generated by the 100 odd systems , the set of the 100 two-graphs is divided into seven classes . The first four classes correspond to the 23 Steiner triple system on 15 points containing a head , i . e . a Fano plane .